Flying Math: Bees Solve Traveling Salesman Problem

Bumblebees foraging in flowers for nectar are like salesmen traveling between towns: Both seek the optimal route to minimize their travel costs. Mathematicians call this the “traveling salesman problem,” in which scientists try to calculate the shortest possible route given a theoretical arrangement of cities. Bumblebees, however, take the brute-force approach: For them, it’s simply a matter of experience, plus trial and error, scientists report in the current issue of PLoS Biology.

The study, the first to track the movements of bumblebees in the field, also suggests that bumblebees aren’t using cognitive maps — mental recreations of their environments — as some scientists have suggested, but rather are learning and remembering the distances and directions that need to be flown to find their way from nest to field to home again.

A team of researchers from Queen Mary, University of London outfitted seven bumblebees with tiny radar transponders, which they stuck on the bees’ backs with double-sided tape. They trained the bees to forage nectar from five blue artificial flowers (see video). Each artificial flower had a yellow landing platform and a single drop of sucrose, just enough to fill one-fifth of a bumblebee’s tank capacity, to ensure that the bees would visit all five flowers on each foraging bout.

The scientists placed the flowers in a field at Rothamsted Research, a biological research station north of London, in October — a time of year when there are few natural sources of nectar and pollen and the bees are more likely to focus on the artificial flowers. They arranged the flowers in a pentagon and spaced them 50 meters apart; that distance is more than three times as far as bumblebees can see, so the bees must actively fly around to locate their next target. A motion-triggered webcam was attached to each flower to record the bees’ visits. Then, every day for a month, each bee was freed to forage for 7 hours.

“We’d done a similar experiment in our lab,” says Mathieu Lihoreau, the lead author of the study and a behavioral ecologist now at the University of Sydney in Australia. “But that was in quite a small area for a bee — only 7 by 7 meters.” Seeing the bees forage in the wild was entirely different. At first, Lihoreau says, he tried to track the bees’ movements by running alongside them as they flew from flower to flower, “but they are so fast, it wasn’t possible.” The transponders eliminated the need for Lihoreau’s sprints, and also collected each bee’s flight trajectory, travel distance, and ground speed. From all those data, the scientists recreated the bees’ journeys and modeled them mathematically — and discovered that they may be employing a relatively simple method to find the most efficient route between the flowers.

“Initially, the bees’ routes were long and complex, and they revisited empty flowers several times,” Lihoreau says. “But they gradually refined their routes through trial and error.”

At first, the bees visited the flower nearest to their nest, and then the next closest flower. They kept track — that is, they remembered — the total distance traveled on each foraging trip. They tried new routes to increase their efficiency, and if a route was shorter, they kept it. If not, they abandoned it. As their experience increased, they rarely altered the sequence of flowers they visited.

After trying about “20 of the 120 possible routes, the bees were able to select the most efficient path to visit the flowers,” Lihoreau says. “They did not need to compute all the possibilities.” A naïve bee traveled almost 2,000 meters on its first foraging bout among the pentagonal array; by her final trip, she’d reduced that distance to a mere 458 meters.

Perhaps most surprising to the scientists was how quickly the bumblebees learned from their trial-and-error method. Before this study, such sophisticated learning was “thought to be something only larger-brained animals were capable of,” says Lars Chittka, a behavioral ecologist at Queen Mary, University London and another member of the team.

Although the researchers did not set out to test whether bumblebees use cognitive maps, the study’s results suggest that they do not. “The idea of a cognitive map is very contentious,” Lihoreau says. “But it’s not a very parsimonious hypothesis; it seems a lot to expect from a small brain with less than one million neurons.” Using a simple rule, as the bumblebees did in this test, may better explain what appears to us as complex behavior, he says.

“It’s a lovely study,” says Mandyam Srinivasan, a neuroethologist at the University of Queensland in Brisbane, Australia. “It shows that bumblebees, with their diminutive 1 milligram brains, are capable of finding a nearly perfect solution to the traveling salesman problem, with relatively few attempts and in a relatively short time.” This doesn’t prove that bumblebees do not possess a cognitive map, he adds, “but it does demonstrate that they can get by without one.”

This story provided by ScienceNOW, the daily online news service of the journal Science.

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